Entropy production as correlation between system and reservoir

TL;DR

This paper derives an exact expression for entropy production in finite classical and quantum systems coupled to reservoirs, linking it to system-reservoir correlations and entanglements, and illustrating the second law at microscopic scales.

Contribution

It introduces a novel exact formulation of entropy production that accounts for correlations and entanglements in finite quantum and classical systems, bridging microscopic reversibility and macroscopic irreversibility.

Findings

Entropy production is always positive and measures system-reservoir correlations.

The model demonstrates the approach to standard irreversibility with large reservoirs.

The formulation applies to both classical and quantum finite systems.

Abstract

We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution. Whereas the total entropy of system plus reservoirs is conserved, we show that the system entropy production is always positive and is a direct measure of the system-reservoir correlations and/or entanglements. Using an exactly solvable quantum model, we illustrate our novel interpretation of the Second Law in a microscopically reversible finite-size setting, with strong coupling between system and reservoirs. With this model, we also explicitly show the approach of our exact formulation to the standard description of irreversibility in the limit of a large reservoir.